Currently, a balance for a watch movement comprises a wheel-shaped part including the felloe (or rim), the arms and a certain arrangement of inertia blocks, which are secured to the felloe of the balance and which, by adjusting their positions, allow the unbalance and moment of inertia of the balance to be altered.
The oscillation frequency f of a sprung balance oscillator is given by the relation:1/f=2π(I/M)0,5 where I is the moment of inertia of the balance about its axis of rotation and M is the resilient couple of the balance spring, expressed in Nm/rad. The usual frequencies of watch oscillators range from 2.5 Hz to 5 Hz, by steps of 0.5 Hz so that a duration of one second corresponds to an integer number of oscillator vibrations. A movement is thus designed for a given frequency and the sprung balance assembly must have that frequency. In the above formula, it can be seen that the pertinent parameter of the balance is the moment of inertia. Since the role of the arms is very limited in the moment of inertia, the latter depends foremost upon the dimensions (diameter and cross section) and density of the felloe and the elements connected thereto.
In some cases, the designer of a timepiece movement may wish to use a balance of relatively large diameters, for example for aesthetic reasons. Increasing the diameter without changing the moment of inertia can be achieved either by decreasing the cross section of the felloe or by using a less dense material. In both cases, the balance will have less mass, which reduces friction in the bearings, and thus interference with the isochronism of the balance depending upon the positions (vertical and horizontal) of the movement. However, a felloe of reduced cross section becomes too weak, especially if it has to carry the adjusting inertia blocks.